One month after it rattled Amazon.com with a slew of deep discounts on best-selling books, Wal-Mart’s Web boss has a warning for any rival who tries to wage another online price war against the retail giant: You will not win.

“If they react and match our prices, we’re going to continue to lower our prices,” said Walmart.com CEO Raul Vazquez in an interview with The Post.

The vow signals that Wal-Mart isn’t afraid to enter the ring once again with Amazon or another online rival as it tries to grab a bigger slice of the online-shopping space for walmart.com, which Vazquez admitted some shoppers call a “best-kept secret.”

Vazquez’s latest warning shot follows a brief, intense skirmish a few weeks ago that brought best-seller prices to around $9 at both Amazon and Wal-Mart’s sites — a move widely seen as a bid by Wal-Mart to beat back Amazon, whose CEO Jeff Bezos has long dreamed of dominating Internet retailing the way Wal-Mart stores have outpaced their competition.

“If there’s going to be a Wal-Mart on the Web, it’s going to be Walmart.com,” Vazquez said, repeating a vow he’s made repeatedly in recent weeks.

While Amazon’s $19.5 billion business is still the biggest online, a source familiar with the matter said sales at Wal-Mart’s Web site this year have grown at a faster rate than Amazon, by about 1.4 percentage points.

Vazquez said he wasn’t surprised by Bezos’ seemingly frantic response when Walmart.com announced it was selling titles like Stephen King’s “Under the Dome” and Dean Koontz’s “Breathless” for just $10.

“In this climate, I think every retailer is doing everything they can to hold onto their customers,” Vazquez told The Post.

“When you’re a mass-market retailer, that’s not a great thing,” Vazquez said. “This is where the recession helped us understand how we could help customers. Now, we realize what the formula is and how to do it well.”